Method for calculating Curie temperature of magnetic material based on first principle and machine learning

Abstract

The invention relates to the cross technical field of material science, computational physics and artificial intelligence, in particular to a method for calculating Curie temperature of a magnetic material based on a first principle and machine learning, which comprises the following steps of: training a machine learning model by using characteristics for describing an atomic chemical environment; predicting the magnetic moment of each atom in the multi-element alloy spin system at the target temperature based on the trained machine learning model; and the change relation of the magnetic susceptibility along with the temperature and the Curie temperature are obtained based on the magnetic moment of each atom in the multi-element alloy spin system at different target temperatures. According to the method, the relation between the complex chemical environment and the magnetic behavior can be learned and captured from a large amount of calculation data by combining a prediction method of machine learning. Compared with a traditional method, the method has more advantages when being used for treating a complex system, and can effectively cope with various variables and complex interactions existing in the multi-element alloy material.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of materials science, computational physics and artificial intelligence, and specifically relates to a method for calculating the Curie temperature of magnetic materials based on first principles and machine learning. Background Technology

[0002] The performance and reliability of traditional magnetic materials face challenges in high-temperature and high-frequency environments. For example, existing magnetic materials may lose magnetism at high temperatures or experience magnetic losses in high-frequency applications, thus affecting the overall performance of devices. Therefore, increasing the Curie temperature of magnetic materials to ensure their stability and reliability under harsh conditions has become an important research topic in materials science.

[0003] First-principles calculations, particularly density functional theory (DFT), have become a mainstream method for new material development and design due to their ability to accurately predict the physicochemical properties of materials without relying on empirical parameters. By calculating the electronic structure and magnetic states of materials, DFT can provide important theoretical basis for the design of new materials. However, when dealing with multi-element alloy magnetic materials, this method typically treats the magnetic moments of the same element as constants. This simplification can lead to prediction errors under different chemical environments, affecting the accuracy of the calculation results. For example, in multi-element alloys, different types and numbers of neighboring atoms can significantly affect the magnetic moment of the central atom. Ignoring this effect often leads to large prediction errors, affecting the accuracy of the calculation results. Summary of the Invention

[0004] In view of the above analysis, the present invention provides a method for calculating the Curie temperature of magnetic materials based on first principles and machine learning, which solves at least one of the problems in the prior art, such as poor prediction accuracy and difficulty in handling multiple variables and complex interactions.

[0005] The objective of this invention is mainly achieved through the following technical solutions:

[0006] A method for calculating the Curie temperature of magnetic materials based on first-principles calculations and machine learning includes:

[0007] The machine learning model is trained based on the features describing the atomic chemical environment; the features of the atomic chemical environment include the element type of the central atom, the types of atoms in the nearest neighbor coordination, the number of atoms in the nearest neighbor coordination, the spin direction angle between the atoms in the nearest neighbor coordination, the types of atoms in the second nearest neighbor coordination, the number of atoms in the second nearest neighbor coordination, and the spin direction angle between the atoms in the second nearest neighbor coordination.

[0008] Predict the magnitude of the magnetic moment of each atom in a multi-element alloy spin system at different target temperatures based on a trained machine learning model;

[0009] The relationship between magnetic susceptibility and temperature, as well as the Curie temperature, was obtained based on the magnetic moment of each atom in the spin system of a multi-element alloy at different target temperatures.

[0010] Preferably, the method for calculating the Curie temperature of magnetic materials based on first-principles calculations and machine learning includes:

[0011] S1: Construct all possible magnetic state structures of multi-element alloys, and calculate the total energy, atomic magnetic moment data and characteristics describing the atomic chemical environment of each magnetic state structure based on first-principles calculations.

[0012] S2: Based on the total energy of each magnetic state structure system, the exchange constants of each atom pair in the Heisenberg spin model are fitted using the linear regression method;

[0013] S3: Use the features describing the atomic chemical environment as input data to form a training dataset; train the machine learning model based on the training dataset;

[0014] S4: Based on a trained machine learning model, predict the magnitude of the magnetic moment of each atom in a multi-element alloy spin system;

[0015] S5: Based on the magnetic moment data predicted by machine learning, the magnetic moment of each atom in the multi-element alloy is set to the predicted value to realize the initialization of the multi-element alloy spin system;

[0016] S6: Select different temperatures within the set temperature range to perform Monte Carlo simulations. Perform multiple Monte Carlo simulations at the target temperature. In each Monte Carlo simulation, randomly select an atom and change its spin direction. Calculate the total energy change ΔE of the multi-element alloy spin system before and after changing the spin direction based on the exchange constant of each atom pair. Continue until the total energy of the multi-element alloy spin system no longer changes, and obtain the equilibrium state of the multi-element alloy spin system at the target temperature.

[0017] S7: Sample multi-element alloy spin systems in equilibrium at different target temperatures, obtain the relationship between magnetic susceptibility and temperature at different target temperatures based on the magnitude of the magnetic moments of atoms in the multi-element alloy spin systems, and determine the Curie temperature Tc.

[0018] Preferably, the construction of all possible magnetic state structures of the multi-element alloy in S1 includes:

[0019] S101: For target multi-element alloy materials, all possible magnetic structures are generated by constructing different atomic arrangements and spin states;

[0020] S102: First-principles calculations were performed on each magnetic state structure using first-principles calculation software to obtain the total energy and magnetic moment data of each atom in each magnetic state structure system.

[0021] Preferably, the total energy H of each magnetic state structure system constructed in S2 according to the following formula satisfies:

[0022] H = H0 - ∑ ij J ij S i S j ;

[0023] Where i and j are the atomic numbers of the atoms in the atom pair, J ij S represents the exchange constant between atomic pairs. i and S j These are the electron spin magnetic moments of the two atoms in the atom pair, which can be calculated using first-principles calculations in S102; H0 is the operator excluding all energies of the exchange interaction, and H is the intercept of the ordinate where H is located obtained by linear regression, which can be obtained by linear regression.

[0024] Preferably, S6 includes: determining the sign of ΔE;

[0025] If ΔE≤0, the atomic spin direction is changed, and the system after the atomic spin direction is changed is output as the spin system of the multi-element alloy at the target temperature;

[0026] If ΔE > 0, a certain probability is used to determine whether to accept or reject the change in atomic spin direction. Preferably, determining the sign of ΔE includes:

[0027] According to the Boltzmann distribution, with probability P = min(1, exp^(-ΔE / K) B T) determines whether to accept or reject the change in the direction of atomic spin, where K B Boltzmann constant;

[0028] When ΔE ≤ 0, P = 1, accepting a change in the spin direction of the atom; when ΔE > 0, P = exp^(-ΔE / K) B T), with probability P determining whether to accept or reject the change in the direction of the atomic spin.

[0029] Preferably, the ΔE calculation satisfies:

[0030] H1=H0-∑ ij J ij S i S j (2);

[0031] H2=H0-∑ ij J ij S i 'Sj '(3);

[0032] ΔE=H2-H1(4);

[0033] Where i and j are the atomic numbers of the atoms in the atom pair, J ij S represents the exchange constant between atomic pairs. i and S j These are the electron spin magnetic moments of the two atoms in the atom pair; S i 'and S j 'H1 represents the electron spin magnetic moments of the two atoms in the atom pair after the spin direction of one atom in the multi-element alloy spin system is changed; H2 represents the total energy of the multi-element alloy spin system before the spin direction of one atom is changed; H3 represents the total energy of the multi-element alloy spin system after the spin direction of one atom is changed.

[0034] Preferably, S7 includes:

[0035] S701: To bring the multi-element alloy spin system to thermal equilibrium at the target temperature;

[0036] S702: Sampling is performed under the equilibrium state of the target temperature to record the magnetic moments of each atom in the spin system of the multi-element alloy at the target temperature, and the magnetic susceptibility at the target temperature is obtained based on the magnetic moments of each atom.

[0037] S703: The relationship between magnetic susceptibility and temperature is obtained based on the magnetic susceptibility at different target temperatures.

[0038] Preferably, obtaining the magnetic susceptibility at the target temperature in S702 includes:

[0039] The formula for calculating magnetic susceptibility χ satisfies:

[0040] Where i is the atomic number of the atom in the atom pair, S i The electron spin magnetic moments of the two atoms in an atom pair are represented by <>, where summation is used.

[0041] Preferably, obtaining the Curie temperature Tc in S7 includes:

[0042] Plot the curve of magnetic susceptibility χ as a function of temperature;

[0043] The Curie temperature Tc is determined by the peak value in the curve.

[0044] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0045] (1) Data-driven predictive capabilities

[0046] Predictive methods incorporating machine learning can learn and capture the relationships between complex chemical environments and magnetic behavior from large amounts of computational data. This data-driven predictive capability makes the method of this invention more advantageous than traditional methods when dealing with complex systems, and can effectively address the multiple variables and complex interactions present in multi-component alloy materials.

[0047] (2) Improve calculation accuracy

[0048] By combining first-principles calculations and machine learning techniques, this invention can accurately predict the magnitude of the magnetic moments of atoms in multi-element alloy magnetic materials. This method overcomes the limitation of traditional calculation methods that treat the magnetic moments of the same element as constants, significantly improving the accuracy of magnetic moment prediction and thus more accurately calculating the Curie temperature of the material.

[0049] (3) Wide applicability of multi-element alloys

[0050] The method of this invention is applicable to multi-element alloy magnetic materials with different compositions and structures. By accurately predicting atomic magnetic moments under different chemical environments, this method can be applied to calculate Curie temperatures in a wide range of material systems, demonstrating strong universality and flexibility.

[0051] (4) Improve material design efficiency

[0052] Using machine learning techniques for magnetic moment prediction can significantly reduce the complexity and computation time of first-principles calculations. Rapidly and accurately predicting the Curie temperature of magnetic materials helps accelerate the development and design cycle of new magnetic materials, improving the efficiency of material design and optimization.

[0053] (5) Enhanced material performance optimization

[0054] This invention provides an effective means to study the magnetic behavior of multi-element alloy magnetic materials under different temperature conditions. By accurately predicting the Curie temperature of the material, its composition and structure can be optimized, enhancing its performance and stability in high-temperature and high-frequency environments, thereby meeting the demand for high-performance magnetic materials in fields such as electronics, aerospace, and high-frequency communications.

[0055] (6) Reduce experimental costs

[0056] Precise computational methods can reduce reliance on actual experiments. Through theoretical prediction and simulation, the magnetic properties of materials can be rapidly screened and evaluated on computers, reducing experimental costs and resource consumption, while also minimizing trial-and-error steps in the materials development process.

[0057] (7) Provide comprehensive material characterization

[0058] This invention, while predicting the Curie temperature, also provides detailed information about the electronic structure, magnetic states, and exchange constants of materials. This information is of significant value for understanding the magnetic mechanisms of materials, designing new materials, and interpreting experimental phenomena.

[0059] In summary, this invention provides an efficient, accurate, and flexible method for predicting the Curie temperature of multi-element alloy magnetic materials by combining machine learning, first-principles calculations, and Monte Carlo simulation techniques. This method not only improves computational accuracy and design efficiency but also possesses broad applicability and data-driven predictive capabilities, providing strong support for the development and performance optimization of novel magnetic materials.

[0060] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objectives and other advantages of this invention can be realized and obtained through the content specifically pointed out in the description. Attached Figure Description

[0061] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0062] in:

[0063] Figure 1 Fe in a 4×4×4 supercell 1-x Co x The body-centered cubic geometry of the alloy;

[0064] Figure 2 A schematic diagram of a machine learning model for predicting the magnetic moments of individual atoms in a material;

[0065] Figure 3a The training set for predicting the magnetic moment of Co-Fe alloys;

[0066] Figure 3b A test set for predicting the magnetic moment of Co-Fe alloys;

[0067] Figure 4a Fe at different temperatures 0.65 Co 0.35 The total magnetic moment M and magnetic susceptibility χ;

[0068] Figure 4b For different components of Fe 1-x Co x The calculated Curie temperature T C ;

[0069] Figure 5 For Fe 78 Co42 The calculated Curie temperature Tc of Zn8. Detailed Implementation

[0070] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which constitute a part of the present invention and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0071] To accurately describe the embodiments of the present invention, the relevant technical terms are further explained as follows:

[0072] This invention proposes a method for calculating the Curie temperature of magnetic materials based on first-principles calculations and machine learning, comprising:

[0073] The machine learning model is trained based on the features describing the atomic chemical environment; the features of the atomic chemical environment include the element type of the central atom, the types of atoms in the nearest neighbor coordination, the number of atoms in the nearest neighbor coordination, the spin direction angle between the atoms in the nearest neighbor coordination, the types of atoms in the second nearest neighbor coordination, the number of atoms in the second nearest neighbor coordination, and the spin direction angle between the atoms in the second nearest neighbor coordination.

[0074] Predict the magnitude of the magnetic moment of each atom in a multi-element alloy spin system at a target temperature based on a trained machine learning model;

[0075] The relationship between magnetic susceptibility and temperature, as well as the Curie temperature, was obtained based on the magnetic moment of each atom in the spin system of a multi-element alloy at different target temperatures.

[0076] Compared to existing technologies, this invention incorporates machine learning-based predictive methods that can learn and capture the relationships between complex chemical environments and magnetic behavior from large amounts of computational data. This data-driven predictive capability gives the method of this invention a significant advantage over traditional methods when dealing with complex systems, effectively addressing the multiple variables and complex interactions present in multi-component alloy materials.

[0077] Specifically, methods for calculating the Curie temperature of magnetic materials based on first-principles calculations and machine learning include:

[0078] S1: Construct all possible magnetic state structures of the multi-element alloy, and calculate the total energy, atomic magnetic moment data, and characteristics describing the atomic chemical environment of each magnetic state structure based on first-principles calculations. The characteristics of the atomic chemical environment include the element type of the central atom, the types of atoms in the nearest neighbor coordination, the number of atoms in the nearest neighbor coordination, the spin direction angle between the atoms in the nearest neighbor coordination, the types of atoms in the second nearest neighbor coordination, the number of atoms in the second nearest neighbor coordination, and the spin direction angle between the atoms in the second nearest neighbor coordination.

[0079] S2: Based on the total energy of each magnetic state structure system, the exchange constants of each atom pair in the Heisenberg spin model are fitted using the linear regression method;

[0080] S3: Use the features describing the atomic chemical environment as input data to form a training dataset; train the machine learning model based on the training dataset;

[0081] S4: Based on a trained machine learning model, predict the magnitude of the magnetic moment of each atom in a multi-element alloy spin system;

[0082] S5: Based on the magnetic moment data predicted by machine learning, the magnetic moment of each atom in the multi-element alloy is set to the predicted value to realize the initialization of the multi-element alloy spin system;

[0083] S6: Select different temperatures within the set temperature range to perform Monte Carlo simulations. Perform multiple Monte Carlo simulations at the target temperature. In each Monte Carlo simulation, randomly select an atom and change its spin direction. Calculate the total energy change ΔE of the multi-element alloy spin system before and after changing the spin direction based on the exchange constant of each atom pair. Continue until the total energy of the multi-element alloy spin system no longer changes, and obtain the equilibrium state of the multi-element alloy spin system at the target temperature.

[0084] S7: Sample multi-element alloy spin systems in equilibrium at different target temperatures, obtain the relationship between magnetic susceptibility and temperature at different target temperatures based on the magnitude of the magnetic moments of atoms in the multi-element alloy spin systems, and determine the Curie temperature Tc.

[0085] Specifically, the possible magnetic state structures for constructing the multi-element alloy in S1 include:

[0086] S101: For target multi-element alloy materials, all possible magnetic structures are generated by constructing different atomic arrangements and spin states;

[0087] S102: First-principles calculations were performed on each magnetic state structure using first-principles calculation software to obtain the total energy and magnetic moment data of each atom in each magnetic state structure system.

[0088] Compared with existing technologies, this invention, by combining first-principles calculations and machine learning techniques, can accurately predict the magnitude of the magnetic moments of atoms in multi-element alloy magnetic materials. This method overcomes the limitation of traditional calculation methods that treat the magnetic moments of the same element as constants, significantly improving the accuracy of magnetic moment prediction and thus more accurately calculating the Curie temperature of the material.

[0089] Furthermore, the method of this invention is applicable to multi-element alloy magnetic materials with different compositions and structures. By accurately predicting atomic magnetic moments under different chemical environments, this method can be applied to calculate Curie temperatures in a wide range of material systems, demonstrating strong universality and flexibility.

[0090] Specifically, the first-principles calculation software in S102 is any one of PWmat, VASP, or Quantum ESPRESSO.

[0091] Specifically, the total energy H (Hamiltonian) of each magnetic state structure system constructed in S2 according to the following formula satisfies:

[0092] H = H0 - ∑ ij J ij S i S j ;

[0093] Where i and j are the atomic numbers of the atoms in the atom pair, J ij S represents the exchange constant between atomic pairs. i and S j These are the electron spin magnetic moments of the two atoms in the atom pair, which can be calculated using first-principles calculations in S102; H0 is the operator excluding all energies of the exchange interaction, and H is the intercept of the ordinate of H obtained by linear regression, which can be obtained by linear regression.

[0094] Specifically, the S3 machine learning algorithm can be any of the following: Bayesian neighbor regression, support vector machine, random forest, or neural network algorithm.

[0095] Specifically, during the training of the S3 machine learning algorithm model, the root mean square error is used to calculate the error between the training output value and the true value.

[0096] Preferably, the root mean square error of the model's predicted magnetic moment is less than 0.1 μm. B (Bohr magneton).

[0097] Specifically, let's take first-principles calculations of iron-cobalt alloys as an example:

[0098]

[0099] Here, symbol represents the element type of the central atom; These represent the number of Fe and Co atoms in the nearest neighbor coordination sites of the central atom, respectively. These represent the number of Fe and Co atoms in the second nearest neighbor coordination of the central atom, respectively. These represent the angles between the spin directions of the central atom and the nearest-neighbor coordinating Fe and Co, respectively; These represent the angles between the spin directions of the central atom and the Fe and Co atoms in the next nearest neighbor coordination sites, respectively.

[0100] Specifically, in S4, the prediction of the magnetic moment of each atom in the spin system of a multi-element alloy includes: taking the features describing the chemical environment of the atom as input data, substituting them into the trained machine learning model, and obtaining the output value of the machine learning model, which is the predicted value of the magnetic moment of each atom in the multi-element alloy.

[0101] Specifically, in S5, the initialization of the multi-element alloy spin system is the process of setting the magnetic moment of each atom in the multi-element alloy to a predicted value.

[0102] Specifically, S6 can use the Metropolis algorithm.

[0103] Specifically, S6 also includes: determining the sign of ΔE;

[0104] If ΔE≤0, the atomic spin direction is changed, and the system after the atomic spin direction is changed is output as the spin system of the multi-element alloy at the target temperature;

[0105] ΔE > 0, which determines whether to accept or reject the change in the direction of atomic spin with a certain probability.

[0106] Specifically, determining the sign of ΔE includes:

[0107] According to the Boltzmann distribution, with probability P = min(1, exp^(-ΔE / K) B T) determines whether to accept or reject the change in the direction of atomic spin, where K B Boltzmann constant;

[0108] When ΔE ≤ 0, P = 1, accepting a change in the spin direction of the atom; when ΔE > 0, P = exp^(-ΔE / K) B T), with probability P determining whether to accept or reject the change in the direction of the atomic spin.

[0109] Specifically, the calculation of ΔE satisfies:

[0110] H1=H0-∑ ij J ij S i S j Equation (2);

[0111] H2=H0-∑ ij J ij S i 'S j Formula (3);

[0112] ΔE = H2 - H1 (Equation 4);

[0113] Where i and j are the atomic numbers of the atoms in the atom pair, J ij S represents the exchange constant between atomic pairs.i and S j These are the electron spin magnetic moments of the two atoms in the atom pair; S i 'and S j 'H1 represents the electron spin magnetic moments of the two atoms in the atom pair after the spin direction of one atom in the multi-element alloy spin system is changed; H2 represents the total energy of the multi-element alloy spin system before the spin direction of one atom is changed; H3 represents the total energy of the multi-element alloy spin system after the spin direction of one atom is changed.

[0114] Specifically, S7 includes:

[0115] S701: Enables the multi-element alloy spin system with the lowest energy at the target temperature to reach thermal equilibrium.

[0116] S702: Sampling is performed under the equilibrium state of the target temperature to record the magnetic moments of each atom in the spin system of the multi-element alloy at the target temperature, and the magnetic susceptibility at the target temperature is obtained based on the magnetic moments of each atom.

[0117] S703: The relationship between magnetic susceptibility and temperature is obtained based on the magnetic susceptibility at different target temperatures.

[0118] Specifically, obtaining the magnetic susceptibility at the target temperature in S702 includes:

[0119] The formula for calculating magnetic susceptibility χ satisfies:

[0120] Where i is the atomic number of the atom in the atom pair, S i The electron spin magnetic moments of the two atoms in an atom pair are represented by <>, where summation is used.

[0121] Specifically, the Curie temperature Tc obtained in S7 includes:

[0122] Analyze the sampling data and plot the curve of magnetic susceptibility as a function of temperature;

[0123] The Curie temperature Tc, which is the temperature at which a material transitions from a ferromagnetic state to a paramagnetic state, is determined by the peak value in the curve.

[0124] Preferably, S7 further includes: S704, recording the total magnetic moment of the multi-element alloy spin system at different target temperatures.

[0125] Specifically, the total magnetic moment in S704 is the sum of the magnetic moments of all atoms in the system. total =∑ i S i Where i is the atomic number in the multi-element alloy spin system, and S i This represents the magnetic moment corresponding to the atomic number.

[0126] When implemented, S704 includes:

[0127] Multiple samples were taken under equilibrium conditions, and the total magnetic moment of the system at different temperatures was recorded.

[0128] The total magnetic moment is the sum of the magnetic moments of all atoms in the system, S. total =∑ i S i .

[0129] Compared with existing technologies, this invention, while predicting the Curie temperature, also provides detailed information about the material's electronic structure (output parameters of step S1), magnetic states (output parameters of step S1), total magnetic moment (output parameters of step S704), and exchange constant (output parameters of step S2). This information is of significant reference value for understanding the magnetic mechanism of materials, designing new materials, and interpreting experimental phenomena, providing comprehensive material characterization.

[0130] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0131] (1) Wide applicability of multi-element alloys

[0132] The method of this invention is applicable to multi-element alloy magnetic materials with different compositions and structures. By accurately predicting atomic magnetic moments under different chemical environments, this method can be applied to calculate Curie temperatures in a wide range of material systems, demonstrating strong universality and flexibility.

[0133] (2) Improve material design efficiency

[0134] Using machine learning techniques for magnetic moment prediction can significantly reduce the complexity and computation time of first-principles calculations. Rapidly and accurately predicting the Curie temperature of magnetic materials helps accelerate the development and design cycle of new magnetic materials, improving the efficiency of material design and optimization.

[0135] (3) Optimization of reinforced material properties

[0136] This invention provides an effective means to study the magnetic behavior of multi-element alloy magnetic materials under different temperature conditions. By accurately predicting the Curie temperature of the material, its composition and structure can be optimized, enhancing its performance and stability in high-temperature and high-frequency environments, thereby meeting the demand for high-performance magnetic materials in fields such as electronics, aerospace, and high-frequency communications.

[0137] (4) Reduce experimental costs

[0138] Precise computational methods can reduce reliance on actual experiments. Through theoretical prediction and simulation, the magnetic properties of materials can be rapidly screened and evaluated on computers, reducing experimental costs and resource consumption, while also minimizing trial-and-error steps in the materials development process.

[0139] In summary, this invention provides an efficient, accurate, and flexible method for predicting the Curie temperature of multi-element alloy magnetic materials by combining machine learning, first-principles calculations, and Monte Carlo simulation techniques. This method not only improves computational accuracy and design efficiency but also possesses broad applicability and data-driven predictive capabilities, providing strong support for the development and performance optimization of novel magnetic materials.

[0140] Example 1: Calculation of Curie temperature in Co-Fe binary alloy system (Bayesian next-neighbor regression)

[0141] Step 1: Select Co x Fe 1-x The mass ratio x of the binary alloy system was determined, and the phase structure of the alloy was determined to be body-centered cubic (BCC). Monte Carlo simulations were used to obtain 5–10 alloy material structures with the lowest energy. Figure 1 ).

[0142] Step 2: Use the obtained low-energy alloy structure as the input file for first-principles calculations using PWM software (other first-principles calculation software can also be selected, such as VASP and Quantum ESPRESSO). Construct alloy structures with different magnetic states using the input file; for example, randomly flip the magnetic moments of 20%, 40%, 60%, and 80% of the Co atoms. Use the first-principles software to calculate the total system energy of the material system under different magnetic states and obtain the magnetic moments of all atoms.

[0143] Step 3: According to the Heisenberg model, H = -∑ i，j I ij S i ·S j Constructing exchange coupling parameters J ij A system of linear equations relating the total energy of the system to the magnetic moment S of the atom. i The values ​​were calculated using first-principles calculations. The exchange coupling parameter J was obtained through linear regression. ij In the Co-Fe system, considering only the interactions between nearest neighbors, we obtain J. Co-Co J Fe-Fe and J Co-Fe Three exchange coupling parameters.

[0144] Step Four: The first-principles calculations in Step Two will yield a large amount of atomic magnetic moment data, which will be used to construct a machine learning model for predicting atomic magnetic moments. Features such as the atom types, coordination numbers, and magnetic moment angles of the nearest and second nearest neighbors will be used. Figure 2 The dataset calculated using first-principles calculations is trained using machine learning methods to obtain a machine learning model that predicts atomic magnetic moments. Figure 3a and Figure 3b When the root mean square error of the model's predicted magnetic moment is less than 0.1 μB (Bohr magnets), which is to achieve the required precision.

[0145] Step 5: Input the exchange coupling parameter J obtained in Step 3 and the machine learning model obtained in Step 4 into the Monte Carlo simulation, set the magnetic moment of each atom in the multi-element alloy to the predicted value, realize the initialization of the multi-element alloy spin system, obtain the equilibrium state and saturation magnetization of the alloy system at different temperatures, and obtain the Curie temperature from the curve. Figure 4a ); for different ratios of Co x Fe 1-x Repeating the above calculations yields Curie temperature curves for Co-Fe alloys with different proportions. Figure 4b ).

[0146] Example 2: Fe 78 Co 42 Calculation of Curie temperature in Zn8 ternary alloy system (neural network algorithm)

[0147] Step 1: Determine Fe 78 Co 42 The phase structure of Zn8 alloy is body-centered cubic (BCC). Monte Carlo simulations were used to obtain 10 alloy material structures with the lowest energy.

[0148] Step 2: Use the obtained low-energy alloy structure as input for first-principles calculations using PWM software. Construct alloy structures with different magnetic states using the input file; for example, randomly flip the magnetic moments of 20%, 40%, 60%, and 80% of the Co and Fe atoms. Calculate the total system energy of the material system under different magnetic states using first-principles software and obtain the magnetic moments of all atoms.

[0149] Step 3: According to the Heisenberg model, H = -∑ i，j J ij S i ·S j Constructing exchange coupling parameters J ij A system of linear equations relating the total energy of the system to the magnetic moment S of the atom. i The values ​​were calculated using first-principles calculations. The exchange coupling parameter J was obtained through linear regression. ij In the Co-Fe-Zn system, considering only the interactions between nearest neighbors, we obtain J. Co-Co J Fe-Fe J Zn-Zn J Co-Fe J Co-Zn J Fe-Zn Six exchange coupling parameters.

[0150]

[0151] Step Four: The first-principles calculations in Step Two will yield a large amount of atomic magnetic moment data. A neural network algorithm will be used to build a machine learning model to predict atomic magnetic moments. Using features such as the atom types, coordination numbers, and magnetic moment angles of the nearest and second nearest neighbors, the dataset from the first-principles calculations will be trained using machine learning methods to obtain the machine learning model for predicting atomic magnetic moments. When the root mean square error of the model's predicted magnetic moment is less than 0.1 μm... B (Bohr magnets), which is to achieve the required precision.

[0152] Step 5: Input the exchange coupling parameter J obtained in Step 3 and the machine learning model obtained in Step 4 into the Monte Carlo simulation, set the magnetic moment of each atom in the multi-element alloy to the predicted value, realize the initialization of the multi-element alloy spin system, obtain the equilibrium state and saturation magnetization of the alloy system at different temperatures, and obtain the Fe from the curve. 78 Co 42 The Curie temperature of Zn8 ternary alloy is 1220K. Figure 5 ).

[0153] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for calculating the Curie temperature of magnetic materials based on first-principles calculations and machine learning, characterized in that, include: The machine learning model is trained based on the features describing the atomic chemical environment; the features of the atomic chemical environment include the element type of the central atom, the types of atoms in the nearest neighbor coordination, the number of atoms in the nearest neighbor coordination, the spin direction angle between the atoms in the nearest neighbor coordination, the types of atoms in the second nearest neighbor coordination, the number of atoms in the second nearest neighbor coordination, and the spin direction angle between the atoms in the second nearest neighbor coordination. Predict the magnitude of the magnetic moment of each atom in a multi-element alloy spin system at a target temperature based on a trained machine learning model; The relationship between magnetic susceptibility and temperature, as well as the Curie temperature, was obtained based on the magnetic moment of each atom in the spin system of a multi-element alloy at different target temperatures.

2. The method for calculating the Curie temperature of magnetic materials based on first-principles calculations and machine learning according to claim 1, characterized in that, The method for calculating the Curie temperature of magnetic materials based on first-principles calculations and machine learning includes: S1: Construct all possible magnetic state structures of multi-element alloys, and calculate the total energy, atomic magnetic moment data and characteristics describing the atomic chemical environment of each magnetic state structure based on first-principles calculations. S2: Based on the total energy of each magnetic state structure system, the exchange constants of each atom pair in the Heisenberg spin model are fitted using the linear regression method; S3: Use the features describing the atomic chemical environment as input data to form a training dataset; train the machine learning model based on the training dataset; S4: Based on a trained machine learning model, predict the magnitude of the magnetic moment of each atom in a multi-element alloy spin system; S5: Based on the magnetic moment data predicted by machine learning, the magnetic moment of each atom in the multi-element alloy is set to the predicted value to realize the initialization of the multi-element alloy spin system; S6: Select different temperatures within the set temperature range to perform Monte Carlo simulations. Perform multiple Monte Carlo simulations at the target temperature. In each Monte Carlo simulation, randomly select an atom and change its spin direction. Calculate the total energy change ΔE of the multi-element alloy spin system before and after changing the spin direction based on the exchange constant of each atom pair. Continue until the total energy of the multi-element alloy spin system no longer changes, and obtain the equilibrium state of the multi-element alloy spin system at the target temperature. S7: Sample multi-element alloy spin systems in equilibrium at different target temperatures, obtain the relationship between magnetic susceptibility and temperature at different target temperatures based on the magnitude of the magnetic moments of atoms in the multi-element alloy spin systems, and determine the Curie temperature Tc.

3. The method for calculating the Curie temperature of magnetic materials based on first-principles calculations and machine learning according to claim 2, characterized in that, All possible magnetic state structures for constructing multi-element alloys in S1 include: S101: For target multi-element alloy materials, all possible magnetic structures are generated by constructing different atomic arrangements and spin states; S102: First-principles calculations were performed on each magnetic state structure using first-principles calculation software to obtain the total energy and magnetic moment data of each atom in each magnetic state structure system.

4. The method for calculating the Curie temperature of magnetic materials based on first-principles calculations and machine learning according to claim 3, characterized in that, In S2, the total energy H of each magnetic state structure system constructed according to the following formula satisfies: H=H0-∑ ij J ij S i S j ; Where i and j are the atomic numbers of the atoms in the atom pair, J ij S represents the exchange constant between atomic pairs. i and S j These are the electron spin magnetic moments of the two atoms in the atom pair, which are obtained through first-principles calculations in S102; H0 is the operator excluding all energies of the exchange interaction, and is the intercept of the ordinate where H is located obtained by linear regression, which can be obtained by linear regression.

5. The method for calculating the Curie temperature of magnetic materials based on first-principles calculations and machine learning according to claim 2, characterized in that, S6 include: Determine the sign of ΔE; ΔE≤0, accepting a change in the spin direction of the atom; ΔE > 0, which determines whether to accept or reject the change in the direction of atomic spin with a certain probability.

6. The method for calculating the Curie temperature of magnetic materials based on first-principles calculations and machine learning according to claim 5, characterized in that, Determining the sign of ΔE includes: According to the Boltzmann distribution, with probability P = min(1, exp^(-ΔE / K) B T) determines whether to accept or reject the change in the direction of atomic spin, where K B Boltzmann constant; When ΔE ≤ 0, P = 1, accepting a change in the spin direction of the atom; when ΔE > 0, P = exp^(-ΔE / K) B T), with probability P determining whether to accept or reject the change in the direction of the atomic spin.

7. The method for calculating the Curie temperature of magnetic materials based on first-principles calculations and machine learning according to claim 6, characterized in that, ΔE calculation satisfies: H1 = H0 - Σ ij J ij S i S j Equation (2); H2 = H0 - Σ ij J ij S i 'S j ' Formula (3); ΔE = H2 - H1 (Equation 4); Where i and j are the atomic numbers of the atoms in the atom pair, J ij S represents the exchange constant between atomic pairs. i and S j These are the electron spin magnetic moments of the two atoms in the atom pair; S i 'and S j 'H1 represents the electron spin magnetic moments of the two atoms in the atom pair after the spin direction of one atom in the multi-element alloy spin system is changed; H2 represents the total energy of the multi-element alloy spin system before the spin direction of one atom is changed; H3 represents the total energy of the multi-element alloy spin system after the spin direction of one atom is changed.

8. The method for calculating the Curie temperature of magnetic materials based on first-principles calculations and machine learning according to claim 2, characterized in that, S7 includes: S701: To bring the multi-element alloy spin system to thermal equilibrium at the target temperature; S702: Sampling is performed under the equilibrium state of the target temperature to record the magnetic moments of each atom in the spin system of the multi-element alloy at the target temperature, and the magnetic susceptibility at the target temperature is obtained based on the magnetic moments of each atom. S703: The relationship between magnetic susceptibility and temperature is obtained based on the magnetic susceptibility at different target temperatures.

9. The method for calculating the Curie temperature of magnetic materials based on first-principles calculations and machine learning according to claim 8, characterized in that, The magnetic susceptibility obtained at the target temperature in S702 includes: The formula for calculating magnetic susceptibility χ satisfies: Where i is the atomic number of the atom in the atom pair, S i The electron spin magnetic moments of the two atoms in an atom pair are represented by <>, where < / > denotes summation.

10. The method for calculating the Curie temperature of magnetic materials based on first-principles calculations and machine learning according to claim 9, characterized in that, The Curie temperature Tc obtained in S7 includes: Plot the curve of magnetic susceptibility χ as a function of temperature; The Curie temperature Tc is determined by the peak value in the curve.

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